Linear carbon chains (LCCs) encapsulated inside the hollow cores of carbon nanotubes (CNTs) have been experimentally synthesized and structurally characterized by Raman spectroscopy and transmission electron microscopy. However, in terms of electronic conductivity, their transportation mechanism has not been investigated theoretically or experimentally. In this study, the density of states and quantum conductance spectra were simulated through density functional theory combined with the non-equilibrium Green function method. The encapsulated LCCs inside (5,5), (6,4), and (9,0) single-walled carbon nanotubes (SWCNTs) exhibited a drastic change from metallic to semiconducting or from semiconducting to metallic due to the strong charge transfer between them. On the other hand, the electronic change in the conductance value of LCCs encapsulated inside the (7,4) SWCNT were in good agreement with the superposition of the individual SWCNTs and the isolated LCCs owing to the weak charge transfer.